各种排序算法总结

暂做笔记，以后再详细整理。

一、插入排序

1、直接插入排序

public class InsertSort {    public static void insertSort(int[] nums) {        int size = nums.length;        for (int i = 1; i < size; i++) {            if (nums[i] < nums[i - 1]) {                int j = i;                int tmp = nums[j];                while (j > 0 && tmp < nums[j - 1]) {                    nums[j] = nums[j - 1];                    j--;                }                nums[j] = tmp;            }        }    }    public static void main(String[] args) {        int[] a = {1,0,63,2,58,42,6,31,12,13,2,13,0,15};        //InsertSort.insertSort(a);        ShellSort.shellSort(a);        System.out.println(Arrays.toString(a));    }}

2、希尔排序

public class ShellSort {    public static void shellSort(int[] nums) {        int gap = nums.length / 2;        while (gap >= 1) {            InsertInShell(nums, gap);            gap /= 2;        }    }    private static void InsertInShell(int[] nums, int gap) {        int size = nums.length;        for (int i = gap; i < size; i++) {            if (nums[i] < nums[i - gap]) {                int j = i;                int tmp = nums[j];                while (j - gap >= 0 && tmp < nums[j - gap]) {                    nums[j] = nums[j - gap];                    j -= gap;                }                nums[j] = tmp;            }        }    }    public static void main(String[] args) {        int[] a = {1,0,63,2,58,42,6,31,12,13,2,13,0,15};        //InsertSort.insertSort(a);        ShellSort.shellSort(a);        System.out.println(Arrays.toString(a));    }}

二、选择排序
1、简单选择

public class SimpleSelectSort {    public static void simpleSelectSort(int[] nums) {        int size = nums.length;        for (int i = 0; i < size; i++) {            int k = selectMin(nums, i, size);            if (k != i) {                int tmp = nums[i];                nums[i] = nums[k];                nums[k] = tmp;            }        }    }    private static int selectMin(int[] nums,int start, int end) {        int k = start;        for (int i = start + 1; i < end; i++) {            if (nums[k] > nums[i]) {                k = i;            }        }        return k;    }    public static void main(String[] args) {        int[] a = {1,0,63,2,58,42,6,31,12,13,2,13,0,15};        //SimpleSelectSort.simpleSelectSort(a);        SimpleSelectSort.selectSort2(a);        System.out.println(Arrays.toString(a));    }}

双向简单选择

public class SimpleSelectSort {    public static void selectSort2(int[] nums) {        int min = 0, max = 0, tmp;        int size = nums.length;        for (int i = 0; i <= size/2; i++) {            max = i;            min = i;            for (int j = i; j < size - i; j++) {                if (nums[max] < nums[j]) {                    max = j;                    continue;                }                if (nums[min] > nums[j]) {                    min = j;                }            }            //最大值在区间最左边，最小值在区间最右边，直接交换两个值就可以了。            if (max == i && min == size - i - 1) {                tmp = nums[min];                nums[min] = nums[max];                nums[max] = tmp;            } else if (max == i) {                //最大值在区间最左边，最小值在区间内。                // 这时候是最左、最右、最小三个值交换                tmp = nums[min];                nums[min] = nums[size - i - 1];                nums[size - i - 1] = nums[max];                nums[max] = tmp;            } else if (min == size - i - 1) {                //最小值再区间最右边，最大值在区间内。                // 这时候也是三个值交换                tmp = nums[max];                nums[max] = nums[i];                nums[i] = nums[min];                nums[min] = tmp;            } else {                //最大值、最小值均在区间内。这时候是四个值交换                tmp = nums[i];                nums[i] = nums[min];                nums[min] = tmp;                tmp = nums[size - i - 1];                nums[size - i - 1] = nums[max];                nums[max] = tmp;            }        }    }    public static void main(String[] args) {        int[] a = {1,0,63,2,58,42,6,31,12,13,2,13,0,15};        //SimpleSelectSort.simpleSelectSort(a);        SimpleSelectSort.selectSort2(a);        System.out.println(Arrays.toString(a));    }}

2、堆排序

public class HeapSort {    public static void heapSort(int[] nums) {        int size = nums.length - 1;        for (int i = (size - 1) / 2; i >= 0; i--) {            adjustHeap(nums, size, i);        }        for (int i = size - 1; i > 0; i--) {            int tmp = nums[i];            nums[i] = nums[0];            nums[0] = tmp;            adjustHeap(nums, i, 0);        }    }    private static void adjustHeap(int[] nums, int size, int pos) {        int lchild = pos * 2 + 1;        int rchild = lchild + 1;        int position = pos;        if (lchild < size && nums[lchild] > nums[pos]) {            position = lchild;        }        if (rchild < size && nums[rchild] > nums[position]) {            position = rchild;        }        if (position != pos) {            int tmp = nums[pos];            nums[pos] = nums[position];            nums[position] = tmp;            adjustHeap(nums, size, position);        }    }    public static void main(String[] args) {        int[] a = {1,0,63,2,58,42,6,31,12,13,2,13,0,15};        HeapSort.heapSort(a);        System.out.println(Arrays.toString(a));    }}

三、交换排序

1、冒泡排序（包括优化后的冒泡和双向冒泡）

public class BubbleSort {    public static void bubbleSort(int[] nums) {        int size = nums.length;        boolean exchange = true;        int band = size - 1;        while (exchange) {            exchange = false;            int k = 0;            for (int i = 0; i < band; i++) {                if (nums[i] > nums[i + 1]) {                    int tmp = nums[i];                    nums[i] = nums[i + 1];                    nums[i + 1] = tmp;                    k = i;                    exchange = true;                }            }            band = k;        }    }    public static void doubleBubbleSort(int[] nums) {        int low = 0;        int high = nums.length - 1;        while (low < high) {            for (int i = low; i < high; i++) {                if (nums[i] > nums[i + 1]) {                    int tmp = nums[i];                    nums[i] = nums[i + 1];                    nums[i + 1] = tmp;                }            }            high--;            for (int i = high; i > low; i--) {                if (nums[i] < nums[i - 1]) {                    int tmp = nums[i];                    nums[i] = nums[i - 1];                    nums[i - 1] = tmp;                }            }            low++;        }    }    public static void main(String[] args) {        int[] a = {1,0,63,2,58,42,6,31,12,13,2,13,0,15};        //bubbleSort(a);        doubleBubbleSort(a);        System.out.println(Arrays.toString(a));    }}

2、快速排序

public class QuickSort {    public static void quickSort(int[] nums) {        sort(nums, 0, nums.length - 1);    }    private static void sort(int[] nums, int left, int right) {        if (left < right) {            int low = left;            int high = right;            int key = nums[left];            while (low < high) {                while (low < high && key <= nums[high]) {                    high--;                }                nums[low] = nums[high];                while (low < high && key >= nums[low]) {                    low++;                }                nums[high] = nums[low];            }            nums[low] = key;            sort(nums, left, low - 1);            sort(nums, low + 1, right);        }    }    public static void main(String[] args) {        int[] a = {1,0,63,2,58,42,6,31,12,13,2,13,0,15};        QuickSort.quickSort(a);        System.out.println(Arrays.toString(a));    }}

四、归并排序

public class MergeSort {    public static void mergeSort(int[] nums, int first, int end, int[] tmp) {        if (first < end) {            int mid = (first + end) / 2;            mergeSort(nums, first, mid, tmp);            mergeSort(nums, mid + 1, end, tmp);            merge(nums, first, mid, end, tmp);        }    }    public static void merge(int[] nums, int first, int mid, int end, int[] tmp) {        int i = first, m = mid, j = mid + 1, n = end;        int k = 0;        while (i <= m && j <= n) {            if (nums[i] <= nums[j]) {                tmp[k++] = nums[i++];            } else {                tmp[k++] = nums[j++];            }        }        while (i <= m) {            tmp[k++] = nums[i++];        }        while (j <= n) {            tmp[k++] = nums[j++];        }        for (int p = 0; p < k; p++) {            nums[first + p] = tmp[p];        }    }    public static void main(String[] args) {        int[] a = {1,0,63,2,58,42,6,31,12,13,2,13,0,15};        MergeSort.mergeSort(a, 0, a.length - 1, new int[a.length]);        System.out.println(Arrays.toString(a));    }}

五、拓扑排序

public class Topological {    public boolean canFinish(int numCourses, int[][] prerequisites) {        Map<Integer, List<Integer>> graph = new HashMap<>();        for (int i = 0; i < numCourses; i++) {            graph.put(i, new ArrayList());        }        for (int[] prerequisite : prerequisites) {            graph.get(prerequisite[1]).add(prerequisite[0]);        }        int[] preNum = new int[numCourses];        for (int i = 0; i < numCourses; i++) {            for (Integer integer : graph.get(i)) {                preNum[integer]++;            }        }        for (int i = 0; i < numCourses; i++) {            int j;            for (j = 0; j < numCourses; j++) {                if (preNum[j] == 0) {                    break;                }            }            if (j == numCourses) {                return false;            }            preNum[j] = -1;            for (Integer integer : graph.get(j)) {                preNum[integer]--;            }        }        return true;    }}